Indirect estimation of alpha-stable distributions and processes
AbstractThe alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its practical usefulness is coupled with a marked theoretical appeal, as it stems from a generalized version of the central limit theorem in which the assumption of the finiteness of the variance is replaced by a less restrictive assumption concerning a somehow regular behavior of the tails. Estimation difficulties have however hindered its diffusion among practitioners. Since simulated values from alpha-stable distributions can be straightforwardly obtained, the indirect inference approach could prove useful to overcome these estimation difficulties. In this paper we provide a description of how to implement such a method by using a skew-t distribution as an auxiliary model. The indirect inference approach will be introduced in the setting of the estimation of the distribution parameters and then extended to linear time series models with alpha-stable disturbances. The performance of this estimation method is then assessed on simulated data. An application on time-series models for the inflation rate concludes the paper.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2004_07.
Length: 23 pages
Date of creation: 01 Jun 2004
Date of revision:
Indirect inference; Alpha-stable distributions; Heavy tails.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-05-23 (All new papers)
- NEP-ECM-2005-05-23 (Econometrics)
- NEP-ETS-2005-05-23 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Marco J. Lombardi, 2004.
"Bayesian inference for alpha-stable distributions: a random walk MCMC approach,"
Econometrics Working Papers Archive
wp2004_11, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February.
- Tauchen, George E. & Gallant, A. Ronald, 1995.
"Which Moments to Match,"
95-20, Duke University, Department of Economics.
- repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
- Gourieroux, C. & Monfort, A. & Renault, E., 1992.
92.279, Toulouse - GREMAQ.
- Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004.
"Constrained Indirect Estimation,"
Review of Economic Studies,
Wiley Blackwell, vol. 71(4), pages 945-973, October.
- Casarin, Roberto, . "Bayesian Inference for Mixtures of Stable Distributions," Open Access publications from UniversitÃ© Paris-Dauphine urn:hdl:123456789/6326, Université Paris-Dauphine.
- Marco Lombardi & Giorgio Calzolari, 2006.
"Indirect estimation of alpha-stable stochastic volatility models,"
Econometrics Working Papers Archive
wp2006_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
- Parrini, Alessandro, 2012. "Indirect estimation of GARCH models with alpha-stable innovations," MPRA Paper 38544, University Library of Munich, Germany.
- Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute, The.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Francesco Calvori).
If references are entirely missing, you can add them using this form.